Assignment 1_Solution

# Assignment 1_Solution - THE UNIVERSITY OF HONG KONG...

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Unformatted text preview: THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1301 PROBABILITY AND STATISTICS I Suggested Solution to Assignment 1 1. Solution to Question A1. (a) 8 × 7 × 6 = 336; (b) ( 8 5 ) = ( 8 3 ) = 8 × 7 × 6 3 × 2 × 1 = 56. 2. Solution to Question A2. (a) The question equals the number of non-negative integer solutions of below equations:        X 1 + ··· + X 6 = 6 ≤ X i ≤ 6 , i = 1 , ··· , 6 , where X i = # { face of a die numbered i appeared among the six dice } , i = 1 , ··· , 6. Thus it is ( 6+6- 1 6- 1 ) = ( 11 5 ) = 11 × 10 × 9 × 8 × 7 5 × 4 × 3 × 2 × 1 = 462. (b) The question equals the number of non-negative integer solutions of below equation: X 1 + X 2 = 6 , subject to ≤ X i ≤ 6 , i = 1 , 2 , 1 where X 1 = # { red face of a die appeared among the six dice } and X 2 = # { blue face of a die appeared among the six dice } ....
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Assignment 1_Solution - THE UNIVERSITY OF HONG KONG...

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